Multi-fractional instantons in SU( N ) Yang-Mills theory on the twisted T 4

Anber, Mohamed M.; Poppitz, Erich

Abstract

We construct analytical self-dual Yang-Mills fractional instanton solutions on a four-torus T4 with ’t Hooft twisted boundary conditions. These instantons possess topological charge Q=rN, where 1 ≤ r < N. To implement the twist, we employ SU(N) transition functions that satisfy periodicity conditions up to center elements and are embedded into SU(k) × SU(ℓ) × U(1) ⊂ SU(N), where ℓ + k = N. The self-duality requirement imposes a condition, kL1L2 = rℓL3L4, on the lengths of the periods of T4 and yields solutions with abelian field strengths. However, by introducing a detuning parameter ∆ ≡ (rℓL3L4 – kL1L2)/L1L2L3L4, we generate self-dual nonabelian solutions on a general T4 as an expansion in powers of ∆. We explore the moduli spaces associated with these solutions and find that they exhibit intricate structures. Solutions with topological charges greater than 1N and k ≠ r possess non-compact moduli spaces, along which the O∆ gauge-invariant densities exhibit runaway behavior. On the other hand, solutions with Q=rN and k = r have compact moduli spaces, whose coordinates correspond to the allowed holonomies in the SU(r) color space. These solutions can be represented as a sum over r lumps centered around the r distinct holonomies, thus resembling a liquid of instantons. In addition, we show that each lump supports 2 adjoint fermion zero modes.

Citation

Anber, M. M., & Poppitz, E. (2023). Multi-fractional instantons in SU( N ) Yang-Mills theory on the twisted T 4. Journal of High Energy Physics, 2023(9), Article 95. https://doi.org/10.1007/jhep09%282023%29095

• Journal Article Type: Article
• Acceptance Date: Sep 7, 2023
• Online Publication Date: Sep 15, 2023
• Publication Date: 2023-09
• Deposit Date: Nov 3, 2023
• Publicly Available Date: Nov 3, 2023
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2023
• Issue: 9
• Article Number: 95
• DOI: https://doi.org/10.1007/jhep09%282023%29095
• Keywords: Anomalies in Field and String Theories, Solitons Monopoles and Instantons, Nonperturbative Effects
• Public URL: https://durham-repository.worktribe.com/output/1876212